Calibration principle of robot tool coordinate system

Tool coordinate system
The default tool coordinate system is based on the flange center point ,XYZ A coordinate system with a fixed direction . Any other tool installed on the end flange ,TCP The position of the point is fixed relative to the center point of the flange , With this TCP Establishing a tool coordinate system for the origin can actually be seen as translation and rotation relative to the end .
calibration
During the use of industrial robots, different tools are often installed on the flange surface of the end of the robot to meet the actual production needs , In order to accurately control the position and attitude of tool movement , It is necessary to calibrate the coordinate system of the tool . The cooperative arm robot I use provides three methods ： Direct input method 、 Four point method and six point method . The four point method is suitable for changing only the origin of the tool coordinate system TCP The location of , Only when the default tool coordinate system is translated . That is, when the new tool is only... Relative to the default coordinate system TCP Location （ namely X、Y、Z） Change , And posture （ namely W、P、R） It hasn't changed , The tool coordinate system can be established by four point calibration method in practical use , The six point method is applicable to the origin of the tool coordinate system （TCP） Your position and posture have changed , When not only the default tool coordinate system is translated but also rotated . When TCP And posture change , Then we need to use the six point method to establish a new tool coordinate system .

Let's focus on “ The six point method ”
1. Calibration procedure
（1） Find a very accurate fixed point within the action range of the robot as the reference point ;
（2） Determine a reference point on the tool （ It's better to be the center point of the tool Tool Center Point, TCP）;
（3） Manual manipulation of robots TCP, With four different tool postures, it just meets the fixed point .
   Any attitude of the first three points , The fourth point is that the reference point of the tool is perpendicular to the fixed point , The fifth point is the tool reference point from the fixed point to the point to be set TCP Of x direction , The sixth point is the tool reference point from the fixed point to the point to be set TCP The in z direction ,（ When taking points, there are x,y Point selection method of direction , Also have x,z Point selection method of direction , It depends on the robot ）, As shown in the figure below ：
  
2. Calibration process
TCP Calibration process


Personally, I think the number in the matrix depends on RPY（z,y,x）, Or Euler angle (z,y,z), Two different approaches , The formula is different , The calculation method can be referred to Introduction to Robotics – Analysis control and application

  because EPT by 3x1 Column vector , And the right side of the equation is 9x3 Matrix , Therefore, the equations are incompatible equations , It is not allowed to directly use the method of solving non-homogeneous linear equations or solve solve . The matrix form of least square method is adopted , One problem with using least squares is that the resulting number is an estimate , There will be some error . Because its coefficient matrix is not a square matrix , No direct inversion , Therefore, the generalized inverse is used . You can use it directly MATLAB The corresponding function is solved , Convenient and quick .
 
Tool coordinate system attitude (TCF) calibration

In the 1 Part of the tool coordinate system has been obtained (TCF) The location of , And calculation TCP The posture adopts z/x Direction calibration .
   The process, TCF Your posture remains the same ( As in the first section – The basic steps are shown in the figure ). Take the first attitude calibration point as the position point 4（ The following figure is marked as the calibration point 1）; The robot moves from the position point 4 set out , Along the +x Move a certain distance in the direction to get the position point 5（ The following figure is marked as the calibration point 2); The robot moves from the position point 4 set out , Along the +z Move a certain distance in the direction to get the position point 6( The following figure is marked as the calibration point 3）. As shown in the figure below ：
  
because 3 One of the calibration points TCF The posture remains the same , so BERi=4,5,6 All equal , And by the (12) have to EPT remain unchanged , Therefore, the tool coordinate system can be obtained T Of x Axial vector X , And ：

obviously ,TCF The minimum condition of six point calibration is that 6 The position and pose of two position points
And to enable the formula to solve , The location point shall be ensured 1,2,3,4 Not on the same plane .

test result
The deviation of translation parameters calculated by the above method is large , The calculation error of multiple groups of data is within ±7cm about ,
So you need to check carefully when using , The angle offset method calculates many groups , forbid . The summary mainly explains the calibration method and general calculation process of tool coordinate system , In actual calibration , Robot comes with calibration calculation , The data can be recorded according to the above six point method , Complete the calibration on the operation box

This data is the final result of calibrating the oil gun at the end of the robot TCP/TCF Parameters , Get the data and adjust it to the tool coordinate system , The parameter sign can be verified by actual operation

principle
For industrial robots , Base coordinates B And Coordinate system of the end flange face T The relationship between them has been set up when making robots , Every time the manipulator is moving , The rotation angle of each joint is changing , Then calculate the coordinate system transformation of each joint , The specific principle can refer to the robot D-H Construction of coordinate system . This paper simplifies the relationship , Assume the base coordinates B Coordinate system with the end flange face E The transformation matrix between is
. The transformation matrix between the tool coordinate system and the end coordinate system is
, The three coordinate systems have the following relationship ：

Because the position relationship between the tool and the end flange surface of the robot is fixed , The calibration process is to calibrate the coordinate system of the robot tool T And robot end coordinate system E The relationship between , It means the position relationship between the tool coordinate system and the robot end coordinate system , The calibration type is similar to hand eye calibration . The calibration process can be divided into two parts , Position of tool center point (TCP) calibration , Tool coordinate system attitude calibration (TCF) .

reference ：
Kang Cunfeng , Wang Hongwei , Zhang Pengfei et al . Research and implementation of tool coordinate system calibration of welding robot [j]. Journal of Beijing University of Technology 2016, 42(1).